The Bernstein-Gel'fand-Gel'fand correspondence is an isomorphism between the derived category of bounded complexes of finitely generated modules over a polynomial ring and the derived category of bounded complexes of finitely generated module over an exterior algebra (or of certain Tate resolutions). This package implements routines for investigating the BGG correspondence.

More details can be found in Sheaf Algorithms Using Exterior Algebra.

- Functions and commands
- beilinson -- Vector bundle map associated to the Beilinson monad
- bgg -- the ith differential of the complex R(M)
- cohomologyTable -- dimensions of cohomology groups
- directImageComplex -- direct image complex
- projectiveProduct -- Makes a product of projective spaces and a system of paramters
- pureResolution -- creates a pure resolution as an iterated direct image
- symExt -- the first differential of the complex R(M)
- tateResolution -- finite piece of the Tate resolution
- universalExtension -- Universal extension of vector bundles on P^1

- Symbols
- Exterior -- dual exterior algebra cached in a polynomial ring
- Regularity -- Option for directImageComplex